Expected value (EV)
Expected value (EV) is the average amount a bet wins or loses per stake if it were repeated an enormous number of times, worked out by weighting every possible result by its probability. In a casino it is almost always negative for the player, because the house edge is built into the payouts. EV describes the long run only, so it says nothing reliable about what happens in a single evening’s play.
How expected value is calculated
The method is to multiply each outcome by its chance of happening, then add the results together, counting losses as negative amounts.
Take a €10 straight-up bet on single-zero roulette. It wins with a probability of one in 37 and pays 35 to 1, so the win side is worth €350 divided by 37. The losing side is worth €10 multiplied by 36 and divided by 37. Subtracting one from the other leaves minus €0.27, which is exactly the 2.7% house edge applied to the stake.
The same sum works for bonuses. A €100 bonus with 35x wagering means €3,500 of play, and at a slot with 96% RTP the expected loss on that turnover is €140, which outweighs the bonus itself. Terms differ between operators, so the figures have to come from the offer actually on the table.
EV compared with RTP and short-term results
RTP and EV measure the same thing from different angles. An RTP of 96% means the expected value of each euro staked is minus four cent, provided the RTP is the version the casino actually runs, since studios often release a game at several settings.
The more common confusion is between EV and what a player sees on the screen. A negative-EV slot can pay out handsomely for an hour, and a high-volatility game will swing far from its average over a few hundred spins. Neither result changes the number, and a losing run does not make a game due to pay.
EV is a long-run average, never a forecast.
